Question:
If vectors $\overrightarrow{a_{1}}=x \hat{i}-\hat{j}+\hat{k}$ and $\overrightarrow{a_{2}}=\hat{i}+y \hat{j}+z \hat{k}$ are collinear, then a possible unit vector parallel to the vector $x \hat{i}+y \hat{j}+z \hat{k}$ is :
Correct Option: , 3
Solution:
$\frac{x}{1}=-\frac{1}{y}=\frac{1}{z}=\lambda($ let $)$
Unit vector parallel to $x \hat{i}+y \hat{j}+z \hat{k}=\pm \frac{\left(\lambda \hat{i}-\frac{1}{\lambda} \hat{j}+\frac{1}{\lambda} \hat{k}\right)}{\sqrt{\lambda^{2}+\frac{2}{\lambda^{2}}}}$
For $\lambda=1$, it is $\pm \frac{(i-3+k)}{\sqrt{3}}$
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